Teaching Physics with the Physics Suite Edward F. Redish

Rollerboards

In the past few years, luggage carts that are rolling suitcases with handles called "rollerboards" have become commonplace in airports around the country. Often, you will see people with a briefcase or additional small bag hung on the cart in one of the two ways shown, either hanging over the front of the cart (Fig. 1) or resting on the handle (Fig. 2). In this problem, we will figure out which way is easier.

In Fig. 3 we have sketched an simplified idealization of the cart as a thin rod with forces acting on it. Three of the forces are shown, the weight of the cart (WE->C), the force of the briefcase on the cart (FB->C), and the force of the traveler's hand holding the cart up (FH->C). Take the angle the cart makes with the ground to be q, the mass of the cart to be M, and the mass of the briefcase to be m. Assume that the total length of the cart, handle and all, is L, the center of gravity of the cart is a distance L1 from the wheel, and the center of gravity of the briefcase is a distance L2 from the wheel.

(a) Find an expression for the force the hand has to exert to hold up the luggage cart. Express your answer in terms of the symbols given above.

(b) Does the force the cart exerts on the floor depend on the positioning of the briefcase? Explain.

(c) Estimate how different the force the hand has to exert would be in the two cases shown in Figs. 1 and 2.

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